Start with the egg yolk in a mixing bowl and add the vinegar. Whisk these two ingredients.
Then slowly (very slowly) add a few drops of the oil in your bowl while still whisking.
Once the mixture starts to thicken add the rest of the oil in a continuous slow stream all while whisking.
When done the homemade mayonnaise should be thick and creamy.
Add the salt and chopped up basil. Mix.